1. Field of the Invention
The present invention relates to object graphics and, in particular, discloses a means by which objects can be described and manipulated by dividing each object into a number of fragments and mathematically describing each fragment by a quadratic polynomial.
2. Description of the Related Art
Most object graphics systems use a frame store to hold a pixel based image of the page or screen. The outlines of individual objects are calculated, filled and written into the frame store. For two dimensional graphics, objects which appear in front of other objects are simply written into the frame store after the background object, thereby replacing the background on a pixel by pixel basis. Such systems are typically expensive in terms of hardware and the time taken to create a full page image.
Real time image generation for raster displays can be achieved by calculating the image in raster order. This means that each scan line must be calculated as it is encountered. This requires that the intersection points of each scan line with each object outline are calculated and then filled.
Traditionally, the calculation of intersections of outlines are performed using straight line or spline formats. The most popular spline formats are various forms of parametric cubic polynomials, such as Bezier curves. If cubic Bezier splines are used, intersection calculation involves calculating the roots of a cubic polynomial at a particular scan line to obtain the parametric positions of the intersections, and substituting these into the polynomial to obtain the actual pixel intersections. Whilst it is possible to build hardware to perform this function in real time, such hardware is highly complex and not suited for consumer priced equipment.